Perhaps there was concern for Tum'ah that day, or the previous night, so the first Haza'ah could not be before day three. The Taharah should have finished on the seventh! If there were many Kelim, so two days were needed for each Haza'ah, they could divide the Mei Chatas into two Kelim, and two people could sprinkle at once! Perhaps they needed another day, for day three or seven was Shabbos; mid'Rabanan, we do not sprinkle on Shabbos. Ein Shevus b'Mikdash does not apply, for Korbanos Tzibur override Tum'ah, if we cannot offer them b'Taharah. (PF)

Is it not better to be Metaher the Kohanim first? They have a Mitzvah to be Tahor, and Taharah permits them to eat Terumah and Kodshim. Also, if a Kohen who needs Haza'ah touches a Kli, the Kli needs Haza'ah (but not vice-versa, unless the Kli touched a Mes - Ohalos 1:3)! And why did they delay Taharas ha'Kohanim? Even if Haza'ah on Kelim took the entire day, they could begin Haza'ah on the Kohanim on day four or five! Were they concerned lest the Mei Chatas finish before sprinkling on all the Kelim? The next Parah Adumah was not until Ezra. We do not find that Mei Chatas ran out after Chizkiyah! However, perhaps there was more Mei Chatas elsewhere. Why did they wait three more days before beginning Haza'ah on Kohanim? Surely they avoided Tum'ah from when Chizkiyah gathered them! The verse says that they needed eight days to be Metaher Beis Hashem - what is Malbim's source that they were also Metaher the Kohanim then? Perhaps since Pesach would be brought b'Tum'ah (there was no time to be Metaher most of Yisrael), they feared lest Kohanim [who want to eat Pesach b'Taharah] distance from Tamei Yisraelim, and not offer their Pesachim. Or, perhaps some Kohanim initially feared to become Tehorim - refer to 29:34:3:1 and the note there. (PF)

Surely, some Kohanim were Tehorim, i.e. they were too young (below 20 years) to serve before Achaz ceased the Avodah, and now they reached the age to serve! (PF)